Move multiple strips in the Video Sequence Editor
Most keyboard shortcuts work on different windows in blender.

A will allow you to select all.

Then if you press G and drag, you can move all the video strips together with the mouse:



To move the strips a specific number of frames use G, then type number of frames you want to move and press Enter. Postitive numbers will move the strips to the right, negative numbers will move them to the left.



The transitions and keyframes will follow the video strips automatically.